import numpy as np
from random import shuffle

def softmax_loss_naive(W, X, y, reg):
  """
  Softmax loss function, naive implementation (with loops)

  Inputs have dimension D, there are C classes, and we operate on minibatches
  of N examples.

  Inputs:
  - W: A numpy array of shape (D, C) containing weights.
  - X: A numpy array of shape (N, D) containing a minibatch of data.
  - y: A numpy array of shape (N,) containing training labels; y[i] = c means
    that X[i] has label c, where 0 <= c < C.
  - reg: (float) regularization strength
    
  Returns a tuple of:
  - loss as single float
  - gradient with respect to weights W; an array of same shape as W
  """
  # Initialize the loss and gradient to zero.
  loss = 0.0
  dW = np.zeros_like(W)

  #############################################################################
  # TODO: Compute the softmax loss and its gradient using explicit loops.     #
  # Store the loss in loss and the gradient in dW. If you are not careful     #
  # here, it is easy to run into numeric instability. Don't forget the        #
  # regularization!                                                           #
  #############################################################################
  num_train = X.shape[0] # 训练的样本数量
  num_classes = W.shape[1] # 分类数量
  for i in range(num_train):
        scores = X[i] @ W #求每一个分类的得分  1 * D  @ D * C
        scores -= np.max(scores) #求分类与最大值的距离 
        sum_scores = np.sum(np.exp(scores)) # 求和
        loss += np.log(sum_scores) - scores[y[i]] #计算损失
        for j in range(num_classes):
            dW[:,j] += (np.exp(scores[j]) / sum_scores) * X[i];
            if y[i] == j:
                dW[:,j] -= X[i]
  dW /= num_train
  dW += reg * W
  loss /= num_train
  loss += 0.5 * reg * np.sum(W * W)
  #############################################################################
  #                          END OF YOUR CODE                                 #
  #############################################################################

  return loss, dW


def softmax_loss_vectorized(W, X, y, reg):
    """
    Softmax loss function, vectorized version.

    Inputs and outputs are the same as softmax_loss_naive.
    """
    # Initialize the loss and gradient to zero.
    loss = 0.0
    dW = np.zeros_like(W)

    #############################################################################
    # TODO: Compute the softmax loss and its gradient using no explicit loops.  #
    # Store the loss in loss and the gradient in dW. If you are not careful     #
    # here, it is easy to run into numeric instability. Don't forget the        #
    # regularization!                                                           #
    #############################################################################
    # *****START OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****
    num_train=X.shape[0]
    num_class=W.shape[1] 
    y_pred=np.dot(X,W)# N * D @ D * C =  N * C
    y_pred=y_pred-y_pred.max(axis=1).reshape(-1,1) 
    softmax_output = np.exp(y_pred)/ np.sum(np.exp(y_pred), axis = 1).reshape(-1,1)#N*C softmax得分
    loss=-np.sum(np.log(softmax_output[range(num_train),list(y)])) 
    loss/=num_train
    loss+=0.5*reg*np.sum(W*W);

    softmax_output[range(num_train),list(y)]+=-1
    dW=(X.T).dot(softmax_output)
    dW=dW/num_train+reg*W
    pass

    # *****END OF YOUR CODE (DO NOT DELETE/MODIFY THIS LINE)*****

    return loss, dW

